Debating cutting another piece of muslin backing to use for side two layout. Side one had both backs available, so the layout on one could be basted to the other row-by-row, which worked out better than sewing with the weight of all the scales pinned in place and stabbing myself every time the angle needed adjustment. A backing piece would be ideal but yardage runs short.
There are spots without as much overlap as I’d like; still deciding if its worth ripping out. Hopefully the heat fusing with alleviate the potential alignment issues.
Thinking about a new EPP project.
In Euclidean geometry, the parallel postulate roughly states: For any line L and point P not on L, there is exactly one line parallel to L that passes through P. This matches our intuitive notion of parallel lines from our everyday experiences (which Euclidean geometry models). But it is not necessary for geometry to include the parallel postulate, and hyperbolic geometry is the consequence of modifying the postulate to allow multiple lines to be parallel to L and pass through P.
Taking a look at both Circle Limit I and Circle Limit III, both images are based on the Poincaré Hyperbolic Disc. In this model of hyperbolic geometry, we work within a circular disk. Lines are represented as circular arcs that intersect the disc at right angles. Circle Limit III highlights these arcs in the white stripes running along the fish. Two hyperbolic lines are considered parallel as long as their arcs don’t intersect. Under this definition, we can confirm that multiple parallel lines can run through the same point — consider the following annotated version of Circle Limit III.
Adkins, Robert. “M.C. Escher and Tessellations“, 1 Feb 2020, math+art.com.
